Group theory is a crucial component of physics teaching，with permutation groups being central to discrete group instruction. The concept of groups is profound and complex，and traditional symbolic and matrix-based representations used in teaching are often not intuitive. This makes it difficult for beginners to grasp the core concepts of group theory. Therefore，there is a necessary for a more intuitive and enlightening method in group theory education to help beginners more easily understand fundamental group-related concepts. In this paper，we introduce an alternative symbolic representation called Stick notation，focusing on the example of the 3-order permutation group. These symbols can intuitively demonstrate essential concepts such as group action，conjugation，commutativity，subgroups，and invariant subgroups. This new and engaging tool has the potential to significantly enhance the effectiveness of group theory education.